T-matrix determination of effective permittivity for three-dimensional dense random media

In this paper, we present a full wave method for determining the effective permittivity for random media in three dimensions. The type of media addressed is composed of spherical dielectric particles in a homogeneous dielectric background. The particle volume fraction ranges from 0 to 40% and dielectric contrast may be significantly different from the background medium. The method described relies on the T-matrix approach for solving Maxwell's equations using a spherical wave expansion in conjunction with a Monte-Carlo simulation for calculating the mean scattered field confined within a prescribed fictitious boundary. To find the effective permittivity, the mean scattered field is compared with that of a homogeneous scatterer whose shape is defined by the fictitious boundary and its dielectric constant is varied until the scattered fields are matched. A complete description of the T-matrix approach is given along with an explanation of why the recursive form of this technique (RATMA) cannot be used for addressing this problem. After the method development is completed, the results of our numerical technique are compared against the theoretical methods of the quasi crystalline approximation and the effective field approximation to demonstrate the region of validity of the theoretical methods. The examples contained within the paper use between 30 and 120 included spheres (with radii ranging from from ka=0.6 to 0.8) within a larger, fictitious sphere of diameter kD=8.4.